Publications related to the GRACE Missions (no abstracts)

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Filtering Unevenly Spaced Geophysical Time Series as an Ill–Posed Problem

Ji, Kunpu, Zhang, Lin, and Wang, Fengwei, 2026. Filtering Unevenly Spaced Geophysical Time Series as an Ill–Posed Problem. Surveys in Geophysics, .

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@ARTICLE{2026SGeo..tmp....3J,
       author = {{Ji}, Kunpu and {Zhang}, Lin and {Wang}, Fengwei},
        title = "{Filtering Unevenly Spaced Geophysical Time Series as an Ill-Posed Problem}",
      journal = {Surveys in Geophysics},
     keywords = {Geophysical time series, Missing data, Fourier filtering, Ill-posed model},
         year = 2026,
        month = jan,
     abstract = "{Irregularly sampled geophysical time series are common in practice due
        to data gaps caused by sensor outages, environmental
        disturbances, or quality control procedures. Conventional
        digital filters, such as Fourier filters, require complete time
        series data and therefore cannot be directly applied to unevenly
        spaced noisy data without prior interpolation. In this study, we
        demonstrate that filtering unevenly spaced time series using
        Fourier filtering is inherently an ill-posed problem, manifested
        as rank deficiency in the associated parametric model. Building
        on this insight, we propose a minimum norm least squares Fourier
        filtering (MFF) that processes unevenly spaced time series
        without the need for preliminary data interpolation.
        Additionally, the prior covariance matrix of the time series is
        incorporated to further improve the filtering performance. We
        first apply the proposed method to extract deformation signals
        from daily position time series of 27 global navigation
        satellite system (GNSS) monitoring stations across the mainland
        China spanning from 1999 to 2024. The performance of MFF is
        compared with conventional Fourier filtering (CFF) with
        interpolation. The results demonstrate that MFF outperforms CFF,
        especially when prior precision is considered, as evidenced by a
        smaller fitting error of the extracted signals. Simulations
        confirm that signals recovered by MFF are closer to the true
        signals, with root mean square error (RMSE) reductions of 12.3
        to 19.4\% across the 27 stations, depending on the percentage of
        missing data. Incorporating formal errors provides an additional
        average RMSE reduction of 2.9\%. Finally, we apply MFF to
        retrieve mass change signals from monthly gravity recovery and
        climate experiment (GRACE) and GRACE-FO gravity field solutions.
        The results agree with those from GNSS time series and show that
        MFF outperforms CFF in extracting components within desired
        frequency bands.}",
          doi = {10.1007/s10712-025-09924-5},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2026SGeo..tmp....3J},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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